Statistical Science

The life and work of Gustav Elfving

Kenneth Nordström

Full-text: Open access

Abstract

This article outlines the scientific work and life of the Finnish statistician, probabilist, and mathematician Gustav Elfving (1908–1984). Elfving’s academic career, scientific contacts, and personal life are sketched, and his main research contributions to the fields of statistics, probability, and mathematics are reviewed. (Elfving’s pioneering work in optimal design of experiments is not covered, as this topic will be treated elsewhere in this issue.) A chronological bibliography of Gustav Elfving is also given.

Article information

Source
Statist. Sci. Volume 14, Number 2 (1999), 174-196.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
http://projecteuclid.org/euclid.ss/1009212244

Mathematical Reviews number (MathSciNet)
MR1722074

Digital Object Identifier
doi:10.1214/ss/1009212244

Zentralblatt MATH identifier
02068900

Citation

Nordström, Kenneth. The life and work of Gustav Elfving. Statistical Science 14 (1999), no. 2, 174--196. doi:10.1214/ss/1009212244. http://projecteuclid.org/euclid.ss/1009212244.


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References

  • Ahlfors, L. V. (1982). Autobiography of Lars V. Ahlfors. In L. V. Ahlfors: Collected Papers, 1929-1955 1 3-7. Birkh¨auser, Boston.
  • Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed. Wiley, New York.
  • Bahadur, R. R. (1955). A characterization of sufficiency. Ann. Math. Statist. 26 286-293.
  • Bakken, I. (1977). A multiparameter eigenvalue problem in the complex plane. Amer. J. Math. 99 1015-1044.
  • Bartlett, M. S. (1933). On the theory of statistical regression. Proc. Roy. Soc. Edinburgh 53 260-283.
  • Bickel, P. and Yahav, J. A. (1969). Some contributions to the asymptotic theory of Bayes solutions. Z. Wahrsch. Verw. Gebiete 11 257-276.
  • Blackwell, D. and Girshick, M. A. (1954). Theory of Games and Statistical Decisions. Wiley, New York.
  • Chiu, W. K. and Wetherill, G. B. (1973). The economic design of continuous inspection procedures: a review paper. Internat. Statist. Rev. 41 357-373.
  • Chow, Y. S., Robbins, H. and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.
  • Chung, K. L. (1960). Markov Chains with Stationary Transition Probabilities. Springer, Berlin.
  • Collins, E. J. and McNamara, J. M. (1993). The job-search problem with competition: an evolutionary stable dynamic strategy. Adv. in Appl. Probab. 25 314-333.
  • Cox, D. R. (1948). A note on the asymptotic distribution of range. Biometrika 35 310-315.
  • David, H. A. (1970). Order Statistics. Wiley, New York.
  • David, I. and Yechiali, U. (1985). A time-dependent stopping problem with application to live organ transplants. Oper. Res. 33 491-504. Draper, N. R., M¨akel¨ainen, T., Nordstr ¨om, K. and Pukels
  • heim, F. (1999). Gustav Elfving: an appreciation. In Statistics, Registries, and Science-Experiences from Finland (J. Alho, ed.). Statistics Finland, Helsinki. To appear.
  • Drasin, D. (1977). The inverse problem of the Nevanlinna theory. Acta Math. 138 83-151.
  • Enns, E. G. and Ferenstein, E. Z. (1990). A competitive bestchoice problem with Poisson arrivals. J. Appl. Probab. 27 333-342.
  • Fraser, D. A. S. (1963). On the definition of fiducial probability. Bull. Internat. Statist. Inst. 40 842-856.
  • Geweke, J., Marshall, R. C. and Zarkin, G. A. (1986). Exact inference for continuous time Markov chain models. Rev. Econom. Stud. 53 653-669.
  • Girshick, M. A. and Rubin, H. (1952). A Bayes approach to a quality control model. Ann. Math. Statist. 23 114-125.
  • Goodman, G. S. (1983). The characterization of mixtures of nonstationary Markov transition matrices. Exposition. Math. 3 283-288.
  • Gumbel, E. J. (1947). The distribution of the range. Ann. Math. Statist. 18 384-412.
  • Gumbel, E. J. (1949). Probability tables for the range. Biometrika 36 142-148.
  • Gumbel, E. J. (1958). Statistics of Extremes. Columbia Univ. Press.
  • Gurland, J. and Asiribo, O. (1991). On the distribution of the multiple correlation coefficient and the kinked chi-square random variable. Statist. Sinica 1 493-502.
  • Hayes, R. H. (1969). Optimal strategies for divestiture. Oper. Res. 17 292-310.
  • Ioannides, Y. M. (1975). Market allocation through search: equilibrium adjustment and price dispersion. J. Econom. Theory 11 247-262.
  • Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions 2, 2nd ed. Wiley, New York.
  • Kingman, J. F. C. (1962). The imbedding problem for finite Markov chains. Z. Wahrsch. Verw. Gebiete 1 14-24.
  • Korn, E. L. (1984). Kendall's tau with a blocking variable. Biometrics 40 209-214.
  • Kshirsagar, A. M. (1972). Multivariate Analysis. Dekker, New York.
  • Lee, Y.-S. (1971). Distribution of the canonical correlations and asymptotic expansions for distributions of certain independence test statistics. Ann. Math. Statist. 42 526-537.
  • Lehmann, E. L. (1986). Testing Statistical Hypotheses, 2nd ed. Wiley, New York.
  • Lieberman, G. J. (1965). Statistical process control and the impact of automatic process control. Technometrics 7 283-292.
  • M¨akel¨ainen, T. (1984). Gustav Elfving. Arkhimedes 36 201-208.
  • M¨akel¨ainen, T. (1997). Elfving, Gustav. In Leading Personalities in Statistical Sciences: From the Seventeenth Century to the Present (N. L. Johnson and S. Kotz, eds.) 96-98. WileyInterscience, New York.
  • Newell, A. D., Blick, D. J. and Hjort, R. C. (1993). Testing for trends when there are changes in methods. Water, Air, and Soil Pollution 67 457-468.
  • Paulson, E. (1969). Sequential interval estimation for the means of normal populations. Ann. Math. Statist. 40 509- 516.
  • Phillips, M. J. (1969). A survey of sampling procedures for continuous production. J. Roy. Statist. Soc. Ser. A 132 205-228.
  • Raiffa, H. and Schlaifer, R. (1961). Applied Statistical Decision Theory. Harvard Univ.
  • Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed. Wiley, New York.
  • Ruben, H. (1963). Probability of a positive sample correlation (abstract). Ann. Math. Statist. 34 694.
  • Ruben, H. (1966). Some new results on the distribution of the sample correlation coefficient. J. Roy. Statist. Soc. Ser. B 32 513-525.
  • Savage, L. J. (1972). The Foundations of Statistics, 2nd rev. ed. Dover, New York.
  • Scarborough, B. B. and McLaurin, W. A. (1964). Saccharin avoidance conditioning instigated immediately after the exposure period. Radiation Research 21 299-307.
  • Siegmund, D. O. (1967). Some problems in the theory of optimal stopping rules. Ann. Math. Statist. 38 1627-1640.
  • Singer, B. and Spilerman, S. (1976). The representation of social processes by Markov models. Amer. J. Sociology 82 1-54.
  • Srivastava, M. S. and Khatri, C. G. (1979). An Introduction to Multivariate Statistics. North-Holland, Amsterdam.
  • Stadje, W. (1987). An optimal k-stopping problem for the Poisson process. In Proceedings of the 6th Pannonian Symposium on Mathematical Statistics (P. Bauer, F. Konecny and W. Wetz, eds.) B 231-244. Reidel, Dordrecht.
  • Stadje, W. (1996). A continuous-time search model with finite horizon. RAIRO Rech. Op´er. 30 233-245.
  • Stuart, A. and Ord, J. K. (1987). Kendall's Advanced Theory of Statistics 1, 5th ed. Griffin, London.
  • Switzer, P. (1992). A conversation with Herbert Solomon. Statist. Sci. 7 388-401.
  • Szab ´o, I. (1967). Magnitude of sound-induced startle response as a function of primary hunger drive. Acta Physiologica Academiae Scientiarum Hungariae 32 241-252.
  • Taylor, J. M. G. (1987). Kendall's and Spearman's correlation coefficients in the presence of a blocking variable. Biometrics 43 409-416.
  • Ury, H. (1968). Photochemical air pollution and automobile accidents in Los Angeles. Archives of Environmental Health 17 334-342.
  • Weibull, J. W. (1978). A search model for microeconomic analysis-with spatial applications. In Spatial Interaction Theory and Planning Models. Studies in Regional Sciences and Urban Economics (A. Karlqvist, L. Lundqvist, F. Snickars and J. W. Weibull, eds.) 3 47-73. North-Holland, Amsterdam.
  • Whitlock, J. H. and Georgi, J. R. (1976). Biological controls in mixed trichostrongyle infections. Parasitology 72 207-224.
  • Wilcoxon, F. (1973). Testing for association between observations. Chemtech 3 364-366.
  • Wilks, S. S. (1932). Certain generalizations in the analysis of variance. Biometrika 24 471-494.